- #1

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## Homework Statement

Let p be an arbitrary polynomial

p(x) = a

_{n}x

^{n}+ a

_{n-1}x

^{n-1}+ ... + a

_{1}x + a

_{0}, a

_{n}cannot equal 0.

a) Find (d

^{n}/dx

^{n})[p(x)]

b)What is (d

^{k}/dx

^{k})[p(x)] for k>n

## Homework Equations

## The Attempt at a Solution

Im actually not really sure what to do for this question.

For the first part i tried to take the first three derivatives and got

(d/dx)[p(x)] = a

_{1}

(d

^{2}/dx

^{2})[p(x)] = 2a

_{2}x + a

_{1}

(d

^{3}/dx

^{3})[p(x)] = 3a

_{3}x

^{2}+ 2a

_{2}x + a

_{1}

(d

^{n}/dx

^{n})[p(x)] = na

_{n}x

^{n-1}+ (n-1)a

_{(n-1)}x

^{n-2}+ ... + a

_{1}

Thats my guess, im not sure of how to do it.

As for part b:

I dont even know how to approach this question, my only assumption is that its the same answer again with all the n's replaced with k's. I am certain this is wrong so please help me do this question both a and b. Thank you.